Explicit Sequences
If a sequence is defined by the formula a(n)=3n+2 what is the value of the 5th term?
17
Write the recursive definition for the sequence 1, 4, 9, 16, ...
This starts @ n=1
a(1)=1;a(n)=a(n−1)+2 n≥2
Write a recursive formula for the following sequence:
0 81
1 27
2 9
f(0)=81 f(n)=f(n-1)*(1/3) n≥1
What is meant by "arithmetic sequence"?
A sequence where each term is obtained by adding a constant value to the previous term.
Create both a recursive and explicit sequence for the following ARITHMETIC sequence:
f(1)=1, f(2)=2
R: f(1)=1 f(n)=f(n-1)+1 n≥2
E: f(n)=1+1(n-1) n≥1
For the sequence defined by a(n)=n2−n what is the value of the 3rd term?
6
Given the sequence defined by a(1)=2 and a(n)=a(n−1)+3 n≥2, what is the 4th term?
11
Write an explicit formula for the following sequence:
1 1
2 2
3 4
f(n)=1*2(n-1) n≥1
What is meant when asked to find the "nth term" of a sequence?
Create the explicit formula for the sequence
Create both an arithmetic and geometric sequence for the following:
f(0)=3 f(1)=6
A: f(0)=3 f(n)=f(n-1)+3 n≥1
G: f(0)=3 f(n)=f(n-1)*2 n≥1
What formula defines the sequence 1, 3, 5, 7, ...?
a(n)=2(n)+1 n>=0
OR
a(n)=2(n-1)+1 n>=1
What recursive equation defines the term of the sequence where each term is half the previous term starting from 64? (n=1)
a(1)=64; a(n)=a(n−1)*(1/2) n≥2.
Write a recursive equation for the following sequence:
0 5
1 10
2 15
f(0)=5 f(n)=f(n-1)+5 n≥1
What is the term for a sequence where each term is derived from the previous term?
Recursive Sequence
Create a geometric and arithmetic sequence for the following in EXPLICIT form:
f(1)=4 f(2)=12
f(n)=4+8(n-1) n≥1
f(n)=4*3(n-1) n≥1
Given the sequence defined as 2, 4, 8, 16, ..., what is the explicit formula?
The explicit formula is
a(n)=2*2n n≥0
OR
a(n)=2*2(n-1) n≥1
Write the recursive formula for the sequence 9,27,81...
n=0
n(0)=9 f(n)=f(n-1)*3 n≥1
Write an explicit equation for the following sequence:
0 81
1 27
2 9
f(n)=81*(1/3)n n≥0
Define the term "common ratio" in a geometric sequence.
The factor by which we multiply to get from one term to the next.
Create both recursive and explicit equations for the following GEOMETRIC sequence:
f(0)=1/4
f(1)=1/2
f(0)=1/4 f(n)=f(n-1)*2 n≥1
f(n)=(1/4)*2n n≥0
Define the sequence a(n)=5n−4 n≥0 first five terms
-4, 1, 6, 11, 16
Write a recursive definition for the sequence given by 3, 8, 15, 24, ...(n=1)
f(1)=3; f(n)=f(n-1) + (2n+1) n≥2
Write an explicit formula for the following sequence:
1 20
2 2.5
3 0.3125
f(n)=20*(1/8)n-1 n≥1
Define what an explicit formula represents in a sequence.
An equation that directly calculates the nth term without referring to previous terms.
Write both explicit and recursive formulas for the following ARITHMETIC sequence:
f(1)=8
f(2)=11
f(1)=8 f(n)=f(n-1)+3 n≥2
f(n)=8+3(n-1) n≥1